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(CBS News) Rumors that the next Apple iPhone is coming on September 12 are beginning to look closer to reality. An executive at the Japanese electronics company Sharp may have let the cat out of the bag.

Screens for the iPhone 5, which will be made by Sharp, are shipping this month, according to the company's president Takashi Okuda.

"Shipments will start in August," Okuda said to the press during an earnings briefing Thursday. Sharp is one of three suppliers, along with LG Display and Japan Display, to make Apple screens, Reuters reports.

The next iPhone screen may be larger - going from 3.5 inches to 4 inches - to rival the Samsung Galaxy S III, which has a 4.8-inch display, according to a Reuters source.

Rumors of a September 12 Apple event began circulating Monday, when the blog iMore reported that Apple will announce two products on that date.

Citing "sources who have proven accurate in the past," the blog reported that Apple may announce an iPhone 5 and iPad mini. According to iMore, the iPhone 5 will go on sale on September 21. There are no details on if or when an iPad mini would be released.

Rumors of an iPad mini with 7.85-inch display have been circulating for some time. Previously, the Chinese blog NetEase reported that Apple has placed an order for an iPad mini. According to the report, 6 million units have been ordered for release in the third quarter. The smaller tablet is estimated to retail anywhere from $249 to $299.

In March, DigiTimesreported that "makers" in Apple's supply chain have started "delivering samples of a 7.85-inch iPads for verification." Weeks later, a report from the Korea Times cited an unnamed Samsung official that corroborated previous reports of a 7.85-inch tablet.